Outcomes with non-equal probabilities

$p_1=p_2=p_3=p_4=p_5=0.2$

Correct

$p_1=p_2=p_3=p_4=p_5=0.1$

$p_1=p_2=0.3$ , $p_3=p_4=p_5=0.1$

$p_1=p_2=0.35$ , $p_3=p_4=p_5=0.1$

Correct

$p_1=0.1,\ p_2=0.2,\ p_3=0.4,\ p_4=0.2,\ p_5=0.1$

Correct

$p_1=-0.1,\ p_2=0.2,\ p_3=0.4,\ p_4=0.3,\ p_5=0.2$

\frac{1}{21}

1/21

Correct

Let $x$ be the probability to get one point. Then the probability to get $k$ points is $kx$ . Sum of all probabilities should be equal to 1, therefore, we have an equation: $x + 2x + 3x + 4x + 5x + 6x = 1$ which is equivalent to $21x=1$ . Therefore, $x = 1/21$

\frac{1}{7}

1/7

Correct

According to previous question, probability to get 1 point is $1/21$ and 2 points is $2/21$ . The probability to get less then 3 points is a sum of probabilities to get 1 point and to get 2 points.

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